Functional Models for Complex and High-Dimensional Data

功能数据分析的创新方法促进了纵向研究、电子商务在线竞标、基因组研究、（生物）人口统计学和许多其他社会、生物和物理科学问题领域的数据分析。所提出的功能方法提供了高度灵活的方法来描述这些数据，特别是研究它们的时间动态方面。研究者将功能数据分析的适用性扩展到在该框架内尚未被广泛考虑的数据结构。这包括点过程，高维（大p，小n）数据和稀疏观察的随机过程，因为它们发生在纵向和重复测量数据中。特别是对于高维的非功能和点流程数据，功能数据分析方法有可能导致变革性的改进，而不仅仅是增量的改进。研究者开发灵活的功能和变系数模型的功能回归和相关。目前的建模方法限制太大，不能广泛适用，需要更通用的模型。同样，曲线翘曲的子领域近年来也有了很大的发展，但仍有许多重要的开放性问题有待研究。研究者将理论分析、模拟和数据应用相结合来进行这项研究，并将方法应用于电子商务、生物人口统计学、纵向研究和基因表达的数据。研究者开发的统计方法对基因组学、人口学和生物人口学中的大型和复杂数据的分析立即有用。这些新的分析工具属于功能数据分析领域，旨在更好地理解时间依赖过程。这些包括各种常见的观察现象，如生长、衰老、在线拍卖期间的出价，或反复观察诸如哮喘发作等反复发生的事件。研究者开发的方法阐明了这种现象的潜在动力学。这些方法的应用使我们能够深入了解老龄化和长寿的机制、在线拍卖的动态以及电子商务的其他实例。研究人员进一步扩展了这些方法的范围，例如，基于受试者基因表达谱的记录，对特定风险的改进预测变得可行。

Innovative methodology for Functional Data Analysis facilitates improved data analysis for longitudinal studies, e-commerce online bidding, genomic studies, (bio)demography and many other areas of the social, biological and physical sciences problems. The proposed functional approaches provide highly flexible ways to characterize such data, and especially to study their time-dynamic aspects. The investigator extends the applicability of Functional Data Analysis to data structures that have not been widely considered within this framework. This includes point processes, high-dimensional (large p, small n) data and sparsely observed stochastic processes as they occur in longitudinal and repeated measurements data. Especially for high-dimensional non-functional and point process data, Functional Data Analysis approaches have the potential to lead to transformative rather than merely incremental improvements. The investigator develops flexible functional and varying-coefficient models for functional regression and correlation. Current modeling approaches are too restrictive to be of broad applicability and more general models are needed. Similarly, the subarea of curve warping has seen much development lately but there remain many important open questions to be investigated. The investigator combines theoretical analysis, simulations, and data applications to conduct this research and applies the methods to data from e-commerce, biodemography, longitudinal studies and gene expression.The investigator develops statistical methodology that is immediately useful for the analysis of large and complex data in genomics, demography and biodemography. These new analysis tools, which fall into the field of Functional Data Analysis, are geared towards gaining a better understanding of time-dependent processes. These include a variety of commonly observed phenomena such as growth, aging, bidding during an online auction, or repeated observations of a recurring incident such as an asthma attack. The methods developed by the investigator elucidate the underlying dynamics of such phenomena. Application of these methods in particular enables insights into the mechanisms of aging and longevity, the dynamics of on-line auctions, and other instances of e-commerce. The investigator extends the scope of these methods further such that for example improved prediction of specific risks becomes feasible, based on a recording of a subject's gene expression profile.